Compressive network coding for wireless sensor networks: Spatio-temporal coding and optimization design
Introduction
Wireless sensor networks (WSNs) consisting of one (or few) sink node(s) and a large number of sensor nodes are usually deployed in a large region to monitor physical or environmental conditions, such as temperature, light, humidity, etc. Since the time-series data of a sensor node usually have temporal dependency, and the observed data of nearby nodes monitoring the same region at the same time slot are highly correlated, the sensor readings usually have both temporal and spatial correlations. Exploiting these correlations can reduce the number of transmissions, and therefore, decrease the energy consumption in WSNs. However, there exist challenges as sensor nodes have limited energy and low computational capability. Fortunately, compressed sensing (CS) [1], [2], [3] transfers most of the computational complexity into the sink node (i.e., reduces the computational burden of sensor nodes), and is considered an effective tool to explore the mutual correlation of sensor readings. Using CS, information can be reconstructed with a high probability of success from a small collection of measurements, which means it can prolong the lifetime of WSNs effectively.
On the other hand, network coding (NC) [4] allows the intermediate nodes to encode the incoming packets rather than simply forwarding them. This powerful theory can improve the network load and enhance network robustness by employing path diversity. So, in addition to prolonging the lifetime of WSNs, NC improves data security. As a result, combining NC and CS for exploiting the correlations of sensor readings in WSNs has become an attractive topic.
The existent research regarding the temporal and spatial correlations in WSNs can be classified into the following four categories.
The first category consists of schemes which exploit either temporal or spatial correlation but not both, such as [5], [6], [7], [8], [9]. Xie et al. [5] used hybrid CS method to propose an analytical model and centralized clustering algorithm for obtaining the minimum number of transmissions in sensor networks. However, the sensing data have considerable redundancy in temporal dimension, and they do not exploit it. The works [6], [7], [8], [9] investigated the correlation of sensing data by combining the NC and CS. Luo et al. [6] proposed a compressive NC for approximate sensor data gathering via exploring the temporal correlation of sensing data. This paper overcomes the all-or-nothing property of NC and achieves graceful degradation in data precisions. Yang et al. [7] designed a compressed NC-based distributed data storage scheme by utilizing the spatial correlation of sensor readings. This scheme possesses an energy-efficient property by reducing the total number of transmissions and receptions. Nabaee et al. [8], [9] constructed a data gathering technique by mining the spatial correlation of sensor data. This technique can achieve a good approximation of the original data with small amount of data received. Similarly, these four works do not consider the temporal and spatial correlations simultaneously which has a significant impact on network efficiency.
The second category includes schemes which study the joint sparsity model-based (JSM-based) spatio-temporal correlations [10], [11], [12], where the temporal and spatial correlations are integrated. In [10], the authors presented a balanced spatio-temporal compression scheme for WSNs. This scheme can reduce energy consumption and prevent overloading of nodes. Chen et al. [11] developed a compressive NC for error control in WSNs. This encoding mechanism can achieve considerable compression ratio and tolerate finite erasures and errors at the same time. In [12], Kong et al. proposed a novel CS-based approach to reconstruct the massive missing data and develop an environmental space time improved CS algorithm to enhance the reconstruction accuracy. The feature of the second category is that the spatial and temporal signals are transformed into a long vector. Although the spatial and temporal correlations are exploited fully, the computational complexity of reconstruction process is high.
The works [13], [14] belong to the third category where the spatial and temporal correlations are both considered and investigated separately. Feizi et al. [13] conceived a power efficient sensing scheme by combining source channel NC and CS. The main merits of this scheme are the low decoding complexity, independent structure and the continuous rate distortion performance. Nevertheless, it assumes that the sampling data of original time-series data still have spatial dependency which is not enough to be convincing. This assumption was eliminated in [14], in which Lee et al. constructed a low complexity sensing for spatio-temporal data. The principle of this scheme is that it samples time-series data in the temporal dimension randomly, and then measures the data in the spatial dimension. It is simple and easy to implement. However, the reconstruction error of this scheme will not be low if the sensor readings fluctuate remarkably among faraway nodes in the same time slot.
Gong et al. [15] formulated the fourth category scheme where the spatial and temporal correlations are both considered and investigated as a unity. The NC scheme in [15] is a spatiotemporal compressive scheme for distributed data storage in WSNs. This scheme can reduce the number of transmissions and receptions, but involves a high computational complexity in the reconstruction process.
Despite the fact that the schemes mentioned above did a lot of meaningful research work in exploration of correlations of sensor readings, all of them (except [6]) only focus on the design of encoding/decoding methods and neglect the optimization of network resource allocation which can improve the network performance significantly.
The network optimization scenario considered in this paper is similar with the resource optimization schemes in NC-based wireless network. Currently, the existing works on optimization of NC-based network resource mainly address the problems of achieving the maximum throughput [16], [17], the maximum lifetime [18], the minimum energy consumption [19], [20], the minimum packet delay [21] and the tradeoff between two randomly former metrics [22], [23], [24].
In [16], [17], the maximum throughput of networks was studied by developing joint congestion control and scheduling with NC. Tan et al. in [18] maximized the network lifetime by optimizing the network flow control and video encoding bit rate jointly. The main goal of works [19], [20] is to minimize the network energy consumption. The work [21] minimized the packet delay in a TDMA-based wireless networks by utilizing NC and successive interference cancelation techniques. The authors in [22] attempted to make a tradeoff between network throughput and energy consumption. In [23], the issue of throughput-delay tradeoff in NC was studied. Also, the tradeoff between network throughput and lifetime was investigated in [24]. These schemes mainly optimize the conventional network performance metrics, however, the more benefits will be obtained when the networks formulate new optimization objective by combining the conventional performance metrics with CS theory. Based on the compressive NC scheme, the work [6] constructed a new optimization objective to improve the performance of compressive NC flows. Although it achieves the optimal network utility, wireless interference will be a big challenge for this scheme.
Motivated by the shortcomings of prior literatures on mining the spatial and temporal correlations and optimizing the network resources, we propose a clustered spatio-temporal compression scheme by combining the NC and CS in WSNs and formulate a new optimization model to make link capacity assignment. The main contributions can be summarized as follows.
One main contribution of our work is that we integrate the CS, NC and spatio-temporal compression into an unified and new system, the NC coefficients and measurement matrix are designed properly for this new system. This design ensures successful reconstruction of original data with a considerably high probability and enables successful deployment of NC and CS in a real field.
The second main contribution is that in contrast to other spatio-temporal schemes with the same computational complexity, the proposed scheme demonstrates lower reconstruction error by developing a new spatio-temporal coding method which employing independent encoding in each sensor node (including the cluster head nodes) and joint decoding in the sink node. At the same time, it has lower computational complexity as compared with JSM-based spatio-temporal scheme and the fourth category scheme by exploiting the temporal and spatial correlations of original sensing data step by step.
Our third main contribution is that we construct a new optimization model for minimizing reconstruction error of the proposed clustered spatio-temporal compression scheme, in which the unreliability of wireless links and the effect of wireless interference are taken into account. The minimization of reconstruction error can be achieved in a distributed manner by utilizing dual decomposition, subgradient algorithm and low-pass filtering method.
Finally, the proposed compression scheme has been verified to have considerable compression gain and lower reconstruction error, and the optimization problem has been validated to converge to the optimal solution with a fast and stable speed.
The remainder of this paper is organized as follows. In Section 2, we introduce basic theory of CS. The network model is defined in Section 3. In Section 4, the proposed compression scheme is given in detail. Section 5 formulates the optimization problem with the goal of minimizing reconstruction error. In Section 6, we analyze the performance of the proposed scheme. Finally, conclusions are drawn in Section 7.
Section snippets
Compressed sensing background
The basic fundamental of CS is that the information can be compressed into a small amount of equivalent information, and then reconstructed successfully with a high probability. For example, consider a signal x of length N that can be represented as for a given matrix Ψ ∈ RN × N and column vector θ ∈ RN. The vector θ is called the coefficient vector. To measure the signal x, we obtain a sampling vector y ∈ Rn by means of a n × N measurement (projection) matrix Φ where n ≪ N.
Now
Network model
In this section, we define the network structure and describe the function of different type nodes.
In our network scenario, we construct a clustered wireless sensor network where a sink node is used to collect the sensing data observed by sensor nodes. The whole sensor network has multiple clusters, and the nearby sensor nodes are allocated into the same cluster where each cluster has a cluster head node. A sensor node in one cluster which has the highest residual energy will be selected as
Clustered spatio-temporal compression scheme
A clustered spatio-temporal compression scheme is developed by extending the work in [8] to a more realistic scenario where sensor readings exhibit both spatial and temporal correlations. The CS, NC and spatio-temporal compression are integrated into an unified and new system. The proper design of NC encoding coefficients and measurement matrix ensures successful reconstruction of original data with a considerably high probability. Meanwhile, the reconstruction error and computational
Optimization design
Reconstruction error is an important performance metric for above compression scheme. Currently, the existent publications improve the reconstruction error mainly by training the sparse dictionary or optimizing the measurement matrix. These papers focus on the design of sparsifying transform and deterministic measurement matrix, which do not consider the network resources and scenario that can impact the reconstruction error significantly. In this section, we formulate a new model to optimize
Performance evaluation
This section provides the performance analysis to show the robustness and efficiency of the proposed clustered spatio-temporal compression scheme and the distributed optimization model in the previous sections.
Conclusion
Based on the temporal and spatial correlations of sensor readings, this paper proposed a clustered spatio-temporal compression scheme to reduce the number of transmissions and formulated a new optimization model to minimize the reconstruction error. The compression scheme could reduce the number of transmissions significantly. In the meantime, the design of NC encoding coefficients and measurement matrix was given for guaranteeing the reconstruction of clustered compression data successfully
Acknowledgment
This work was partially supported by the National Natural Science Foundation of China (Nos. 61201160, 61471025, 61373135, 61672299), the Natural Science Foundation of Jiangsu Province (No. BK20131377), the China Scholarship Council Project (No. 201408320091), Six Talented Eminence Foundation of Jiangsu Province (No. XYDXXJS-044) and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (No. NY213048).
Siguang Chen is currently an Associate Professor at Nanjing University of Posts and Telecommunications. He received his Ph.D. in information security from Nanjing University of Posts and Telecommunications, Nanjing, China, in 2011. He finished his Postdoctoral research work in City University of Hong Kong in 2012. From 2014 to 2015, he also was a Postdoctoral Fellow in the University of British Columbia. His research interests are in the area of dependable and secure network coding, wireless
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2019, Computer NetworksCitation Excerpt :For WSNs deployed in square area or circular area, Nguyen et al. put forward a compressive sensing-based random walk data collection (CSR) algorithm [28]. Apart from this work, there are also the cluster-based compressive data gathering methods [29–31]. For instance, Nguyen et al. [31] proposed a Cluster-Based Compressive Sensing Data Collection (CCS) algorithm, of which the measurement matrix was a block diagonal matrix.
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2019, Journal of Network and Computer ApplicationsCitation Excerpt :However, these efforts did not consider clustering, which can further identify spatial correlation among sensor nodes. To address the limitations of the second-category schemes, refs. (Eskandari et al., 2016; Chen et al., 2015, 2016b, 2018a) developed a third category in which a clustering compression scheme based on spatial and temporal correlations was proposed. In (Eskandari et al., 2016), Eskandari et al. constructed an optimal clustering algorithm; their scheme uses two different types of linear programming techniques to obtain high recovery precision and low energy consumption of transmission.
Siguang Chen is currently an Associate Professor at Nanjing University of Posts and Telecommunications. He received his Ph.D. in information security from Nanjing University of Posts and Telecommunications, Nanjing, China, in 2011. He finished his Postdoctoral research work in City University of Hong Kong in 2012. From 2014 to 2015, he also was a Postdoctoral Fellow in the University of British Columbia. His research interests are in the area of dependable and secure network coding, wireless network resource optimization and the interplay between network coding and compressed sensing.
Chuanxin Zhao is currently a Research Associate at Curtin University and an Associate Professor at Anhui Normal University. He received his Ph.D. in computer science from Suzhou University, Suzhou, China, in 2012. His main research interests include network coding and wireless network resource management and Optimization.
Meng Wu received his B.S., M.S. and Ph.D. degrees in communication engineering and computer science from Zhenjiang University, Shanghai Jiaotong University, Southeast University, in 1985, 1990 and 1993, respectively. Currently, he is a Professor of Nanjing University of Posts and Telecommunications. His main research areas are wireless communications, secure network coding, sensor network and the related information security.
Zhixin Sun received his Ph.D. from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1998. He finished his postdoctoral research work in Seoul National University in 2002. Currently, he is a Professor of Nanjing University of Posts and Telecommunications. His current research interests include computer network and security, network multimedia communications and network management and protocol.
Haijun Zhang received his Ph.D. degree from Beijing University of Posts Telecommunications (BUPT). He hold a Postdoctoral Research Fellow position in Department of Electrical and Computer Engineering, the University of British Columbia (UBC). He was an Associate Professor in College of Information Science and Technology, Beijing University of Chemical Technology. From 2011 to 2012, he visited Centre for Telecommunications Research, King’s College London, London, UK, as a joint PhD student and Research Associate. He has published more than 50 papers and has authored 2 books. He serves as the editors of Journal of Network and Computer Applications, Wireless Networks (Springer), and KSII Transactions on Internet and Information Systems. He served as Symposium Chair of GAMENETS’2014 and Track Chair of ScalCom’2015. He also serves or served as TPC members of many IEEE conferences, such as Globecom and ICC. His current research interests include 5G, Resource Allocation, Heterogeneous Small Cell Networks and Ultra-Dense Networks.
Victor C.M. Leung is a Professor of Electrical and Computer Engineering and holder of the TELUS Mobility Research Chair at the University of British Columbia (UBC). His research is in the areas of wireless networks and mobile systems. He has coauthored more than 800 technical papers in archival journals and refereed conference proceedings, several of which had won best paper awards. Dr. Leung is a Fellow of IEEE, a Fellow of the Royal Society of Canada, a Fellow of the Canadian Academy of Engineering and a Fellow of the Engineering Institute of Canada. He is serving or has served on the editorial boards of JCN, IEEE JSAC, Transactions on Computers, Wireless Communications, and Vehicular Technology, Wireless Communications Letters, and several other journals. He has provided leadership to the technical program committees and organizing committees of numerous international conferences. Dr. Leung was the recipient of the 1977 APEBC Gold Medal, NSERC Postgraduate Scholarships from 1977 to 1981, a 2012 UBC Killam Research Prize, and an IEEE Vancouver Section Centennial Award.